DEPARTMENT OF COMMERCE 



Technologic Papers 



OF THE 



Bureau of Standards 

S. W. STRATTON, Director 



No. 218 

[Part of Vol. 16] 

RESULTS OF SOME COMPRESSION TESTS 
OF STRUCTURAL STEEL ANGLES 

BY 

A. H. STANG, Associate Physicist 

L. R. STRICKENBERG, Assistant Mechanical Engineer 

Bureau of Standards 



AUGUST 3, 1922 




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Washington, D. C. 

WASHINGTON 

GOVERNMENT PRINTING OFFICE 

1922 



AbboT** 1 



DEPARTMENT OF COMMERCE 



Technologic Papers 



OF THE 



Bureau of Standards 

S. W. STRATTON, Director 



No. 218 

[Part of Vol. 16) 

RESULTS OF SOME COMPRESSION TESTS 
OF STRUCTURAL STEEL ANGLES 

BY 

A. H. STANG, Associate Physicist 

L. R. STRICKENBERG, Assistant Mechanical Engineer 

Bureau of Standards 



AUGUST 3, 1922 




PRICE, 10 CENTS; $1.25 PER VOLUME 

Sold only by the Superintendent of Documents. Government Printing Office 
Washington, D. C. 

V/ASHINGTON 

GOVERNMENT PRINTING OFFICE 

1922 



s h 



vp 



LIBRARY OF CONGRESS 
RECEIVED 

OCT 4 1922 

DOCUMENTS DIV)o»<> 






RESULTS OF SOME COMPRESSION TESTS OF 
STRUCTURAL STEEL ANGLES. 

By A. H. Stang and L. R. Strickenberg. 



ABSTRACT. 

This article presents the results of compression tests of 170 structural angles, made 
at the Pittsburgh branch, Bureau of Standards. The object of the tests was to 
determine the ultimate compressive strength of angles fastened at the ends in such 
ways as would closely correspond to their connections in the construction of trans- 
mission towers. There was also tested a series of angles with square ends. An end 
fixation factor was found to represent satisfactorily the effect of different types of. 
end connections. Using this fixation factor, the average values for large slenderness 
ratios were well represented by Euler's formula. The results obtained from shorter 
columns agreed with the experimental and theoretical results of Karman. The 
effect of eccentric loading was most marked at the slenderness ratios indicated by 
Karman 's theory. 

CONTENTS. Page 

I. Introduction 651 

II. Methods of testing 652 

III. Results and discussion of tests 671 

IV. Conclusions 677 

I. INTRODUCTION. 

Compression tests of 170 standard rolled structural steel angles 
were made at the Pittsburgh laboratory of the Bureau of Standards 
during the spring of 1 9 1 7 . The specimens tested were all furnished 
by the tower department of the American Bridge Co., which coop- 
erated in planning the investigation and in carrying out the tests. 
As the angles were intended for legs and lattice members in elec- 
trical transmission tower construction, the greater number were 
tested with bolted ends, the bolting imitating the riveting used in 
the construction of the towers. For comparison a number of 

angles were also tested with flat ends. 

651 



652 



Technologic Papers of the Bureau of Standards. [Vol. 16 



II. METHOD OF TESTING. 

The specimens were all tested in a 600,000-pound Olsen testing 
machine. (Fig. 1 shows a general view of the testing machine 
with an angle under load.) In order to determine the deforma- 
tion that took place in the angle as the load was applied, a special 
compressometer was used which was so located as to measure the 
shortening of the centroidal axis of the specimen. A view of the 
compressometer attached to a test specimen is shown in Figure 2. 

The angles with square ends, having no bolts, were mounted 
directly between the base and the straining head of the testing 
machine. In order to test the bolted specimens, special fixtures 
of structural material were bolted to the base and straining head 
of the machine. and the specimens bolted to these, as shown in 
Figure 2, a view of the connection used for two bolts in one leg of 
the angle. A specimen with ends folded is shown in Fig. 3. 

The dimensions of the angles are shown in Tables 1 to 7, in- 
clusive, and in Figures 4 to 15 accompanying them. The physical 
and chemical properties of the material in the angles, obtained in- 
completely from the mill test reports, are given in Table 8. 



TABLE 1. — Results of Compression Tests on Angles with Square 

Ends, No Bolts. 



21 



Fig. 4. 



Specimen 


Length 
L. 


Size angle. 


Maximum load (lbs./in. 2 ) for slendeiness ratio l/r= 


No. 


50 


100 


150 


200 


250 


300 


350 


Al 


Ft. in. 
S 

10 
15 

2 sy 2 

4 11 

7 4Y 2 
9 10 

12 3J4 

14 9 

17 zy 2 

5 9 

11 6 
17 3 


Inches. 
3 by 3 by A 




40,000 












A2 


3 by 3 by A 






26, 800 








A3 


3 by 3 by A 










10, 750 




A4 


3by3byM 

3by3byM 


37, 000 












AS 


36, 000 












A6 


3 by 3 by \i 




32, 500 










A7 


3by3byM 






25, 000 








A8 


3by3byM 








16, 580 






A9 


3 by 3 by M 










10, 750 




A10 


3 by 3 by J^... 












9 000 


All 


3V£by3HbyJi-... 




33, 000 












A12 


314 by 3J4 by M . . 






22,500 








A13 


314 by 3'A by H-. 










12,660 






















37, 000 


36, 300 


32, 500 


24, 800 


16,580 


11,390 


9,000 











Technologic Papers of the Bureau of Standards, Vol. 16. 




Fig. i. — View of the testing machine with an angle under load. 



Technologic Papers of the Bureau of Standards, Vol. 16. 




Fig. 3. — An angle with ends folded, 
in the testing machine. 



Fig. 2. — View of compressometer and 
connections used for fastening a 
test specimen to the testing machine, 
two bolts in one leg. 



Slang \ 

Strickenbergi 



Compression Tests of Structural Angles. 



653 



1+ i[rr~^i h 

TABLE 2.— Results of Compression Tests on Angles with One Hr iT^ ?*^ 
Bolt Connection, Plain Ends. 



Fig. S- 



Specimen 
No. 



Bl 

B2 

B6 

B7 

B8 

B9 

BIO 

Bll 

B12 

B13 

B14 

B17 

B18 

B19 

B30 

B21 

B22 

B23 

B24 

B25 

B26 

B27 

B28 

B29 

B29A 

B30 

B30A 

BX30 

B31 

BX31 

B32 

BX32 

B33 

B34 

B35 

B36 

B37 

B38 

B39 

Averag 



Length 
L. 



Ft. in. 

4 4H 



5H 

2V 2 
2V 2 

5V 2 



8 6^ 

10 zy 2 

8 6y 

10 V/ 2 

10 iy 2 

12 zy 2 

14 9^ 

12 sy 2 

10 5 

12 sy, 

14 6 

12 sy 

is zy 2 

17 sy 

15 zy 2 
is zy 

12 6 

12 6 

12 6 

14 \\y 2 

14 \\y 2 



17 sy 

20 4 

17 sy 

20 4 

u $y 

13 sy 

15 11^ 



Dis- 
tance. 
M. 



Ft. 
4 
6 
4 
6 
5 



in. 

2 

3 









6 3 

7 6 

4 10 

7 3 

8 4 

10 
8 4 
10 
10 5 
12 6 



14 
12 



10 zy 

12 3 

14 3y 

12 6 

15 



17 
15 
15 



12 3V 2 

12 3J4 

12 3y 

14 9 

14 9 

17 2y 

17 2^ 

17 3 

20 \y 2 

17 3 

20 iy 

11 3 



13 
15 



Size angles. 



Inches. 
lHbylHbyy. 
lUbyiybyy. 
lJibyl^byA. 
l}4byl>£byA- 
iy by \y 2 by 34 

lybyiybyy. 

iybyiyt>yy 

VAbyiyby^ 
\yby\y 2 by-h. 
2 by 2 by >g 

2 by 2 by H 

2by2byA 

2 by 2 by A 

zy by ZV 2 by y 

zybyzybyy 

zy by 2J^ by 34 
zy 2 by 2^ by A 
214 by 2^ by y 
zy by 2^ by y. 
zybyzybyy 

3by3by^ 

3by3by>S 

3by3byM 

3by3byA 

3by3byA 

3 by 3 by M 

3 by 3 by M-... 

3by3byM 

3by3byM 

3by3byM 

3 by 3 by y 

3by3byM 

3y by iy by A 
3y by 3y 2 by A 
3y 2 by 3^ by M 

3Hby3J^byM 
3H by 234 by M 
334 by 23^ by y 
3y by 2^ by H 



Dis- 
tance. 
N. 



Inches. 



8 

« 
+1 
1 

1 

1 

1 

M 

1M 

1M 

1M 

iy 

1M 

1^ 
1H 
iy 

ry 
m 
iy 
ih 
\y 

iy 
iy 
iy 

iy 

m 

1M 

m 

\y 



Diam- 
eter of 
holes. 



Inch. 

9 

T5 

A 



i* 

a 
a 

H 
H 
ft 
ft 

ft 
ft 
ft 
ft 
ft 

ft 
ft 
ft 
ft 
ft 

ft 
ft 
ft 
ft 
ft 

ft 
ft 
ft 
ft 
ft 

ft 
ft 
ft 
ft 



Maximum load (lbs./in. 2 ) for 
slendemess ratio l/r= 



200 



9,070 



10,710 



8,500 



10, 150 



250 



6,460 



5,210 



5,500 
"5,566 



6,000 



4,670 



9,610 



5,500 
5,400 
5,420 



5,000 



5,460 



300 



5,380 



5,250 



4,660 
"i,"956' 



4,000 
"4,450 



3,350 



4,000 
*4," 760 



3,150 



3,890 
3,880 



3,930 
4,450 



4,000 
"3," 540 



3,410 



4,240 



350 



2,610 



3,320 



2,210 



2,750 
3,270 



2,920 

2,720 



3,500 



2,910 



#T-C-. 



TABLE 3.— Results of Compression Tests on Angles with One 
Bolt Connection in One Leg Only, Ends Folded. 



-3-r# 



*^C 



^H if 



Fig. 6. 



^^ 



Specimen No. 


Length 
L. 


Distance 
M. 


Size angle. 


Dis- 
tance 
N. 


Diam- 
eter of 
holes. 


Maximum load (lbs./ 
in. 2 ) for slendemess 
ratio l/r= 




100 


200 


300 


B3 


Ft. in. 

2 3y 2 

4 *y 

6 103^ 

10 234 


Ft. in. 
2 1 
4 2 
6 8 

10 


Inches. 

lMbyl^by}^ 

l^byl)ibyi^ 

2 by 2 by y 


Inch. 

% 
% 

1 

1 


Inch. 
9 

A 

ft 

a 


14, 900 






B4 


9250 
7400 




B15 




B16 


2 by 2 by y 


4500 














14, 900 


8325 45nn 








1 









654 



Technologic Papers of the Bureau of Standards. 



[Vol. 16 



~H'r- ~2i'- 



TABLE 4.— Results of Compression Tests on Angles with Two ^CpSEjjLjrH 8 
Bolt Connections, One Leg Only, Plain Ends. ] 1 



Fig. 7. 



Specimen 
No. 



Length 
L. 



Dis- 
tance. 
M. 



Size angles. 



Dis- 
tance. 

N. 



Diam- 
eter of 
holes. 



Maximum load (lbs./in. 2 ) for 
slendemess ratio l/r= 



100 



150 



200 



250 



CI.. 
C2.. 
C3.. 
C3a. 
C4.. 



C5.. 

C6... 
C7... 
C8.. 
Cll. 

C12. 
C13. 
C14. 
C15. 
C16. 

C17. 
C18. 
C19. 
C20. 
C21. 



C21a. 
C22.. 
C22a. 
C23.. 
C23a, 



C24... 
C24a. 
C25.. 
C25a. 
C26.. 



C27... 
C28-. 
C28a. 
C29.. 
C29a. 

C30.. 
C30a. 
C31.. 



Average. 



Ft. in. 

2 5% 
2 4% 
2 10% 
2 10% 
4 1% 

2 9% 

4 OH 

5 4% 
7 0% 
5 4% 



OH 

7% 



s s% 

6 6% 

8 6% 

6 6% 

8 6H 

7 10% 
10 4% 
10 4% 

10 4% 

7 m 

7 9% 

10 2% 

10 2% 

10 2% 

10 2% 

12 8% 

12 834 

11 10% 

14 9% 

11 10% 
11 10% 

14 9% 
14 9% 

14 9% 
14 9J4 

9 4% 



Ft. in. 

1 10% 

1 9% 

2 3% 

2 3% 

3 6% 

2 2% 

3 5J4 

4 9% 
6 5% 

4 9% 

6 5% 

6 0% 

8 1% 

sun 

7 11% 

5 11% 
7 11% 
7 3% 

9 9% 
9 9% 

9 9% 
7 2% 
7 2% 
9 7% 
9 7% 



7% 
7% 



12 1% 
12 1% 
11 3% 

H 2% 
11 3% 
3% 
2% 
14 2% 



li 



14 in 

14 2% 
8 9% 



Inches. 
l%byl%by^... 

lJOyl^bytV... 
lHbyl^byJ^... 
iy 2 bylAbyy 8 ... 
iH^yVAbyVs... 

V4byiy 2 by&... 

l^byl^byA-.- 
2by2byJ^ 

2by2byH 

2by2byA 



2by2byA 

2% by 2V 2 by%. 
2V 2 by 2y 2 by y s . 
2V 2 by iy 2 by -h . 
2y 2 by iy 2 by A . 

2^ by ty 2 by % . 

2^by2^byM-. 

3by3byH---- 
3by3by>g 

3by3byA 



3 by 3 by A - 
3 by 3 by M . 
3 by 3 by H - 
3 by 3 by M . 
3 by 3 by % . 



3by3by^ 

3 by 3 by A 

3by3by^ 

3by3by^ 

3J4by3^byA. 

V/ 2 by zy 2 by A- 
3^by3^by%. 
3J^ by 3% by % . 
3i4 by 3l4byH- 
3V 2 byZy 2 byH- 

V/ 2 by 3H by A ■ 
3^ by zy 2 by A • 
3^by2J^by%. 



Inches. 



« 

« 
« 

1 
1 
1 

1 

1% 
1% 
VH 
1% 

1% 
1% 

m 

m 
m 
\y 2 

m 

m 

m 
m 

m 

m 



Inch. 

A 

« 

it 
a 

a 
« 

ft 

it 

« 
it 

it 
it 
H 

it 
H 

it 
it 
it 

it 
H 
it 
it 



H 

it 
it 

a 

H 

it 
« 

H 

■H 
it 

it 
it 
H 



27, 200 
24, 200 
23, 500 
24,000 



19, 470 



26,900 



23, 400 
15,350 



18,500 



13, 800 
17,' 250 



16,995 
12,466 



15, 210 
16, 400 



14, 500 



14, 200 
l6,'9i6 
13,830 



12,780 



8,950 
12, 520 

13, 400 



11,700 
12,530 

11,800 
12,570 



11,300 



9,870 
10, 400 



25, 200 



16, 880 



11,800 
12,050 



10, 000 
8,350 



8,350 



6,300 
7,850 

8,800 
9,100 



8,400 



stang i Compression Tests of Structural Angles. 

Strickenberg} . r 



2*:=- 



655 






TABLE 5.— Results of Compression Tests on Angles with Two *-£=?. 
Bolt Connections, One Leg Only, Ends Folded. 



Fig. 8. 



Specimen No. 



C9.. 

CIO. 



Length 
L. 



Ft. in. 

2 OH 

3 8M 



Distance 

M. 



Ft. in. 

1 5M 
3 1M 



Size angle. 



Inches. 

2by2byJ^ 

2 by 2\>yy 8 



Diameter 
of holes. 



Maximum load (lbs./ 

in. 2 ) for slenderness 

ratio l/r= 



Inch. 



50 



16, 530 



100 



18,000 



TABLE 6.-Results of Compression Tests on Angles with Two Bolt Connections, 

One Bolt in Each Leg. 



Fig. 9- 
Specimens No. D1-D10. 



Fig. 10. 
Specimens No. E1-E8. 



Specimen 
No. 


Length 
L. 


Distance 
M. 


Size angle. 


Diameter 
of holes. - 


Maximum load (lbs./in. 2 ) for slenderness 
ratio l/r= 


200 


250 


300 


350 




Ft. in. 
10 3 
12 9 
10 1 
10 1 

12 f>y 2 

12 6)4 
10 1 

10 1 

11 9 

14 m 

17 6 
14 1Yi 
17 6 
16 %\4 
20 

23 zy 2 

20 
16 814 
20 

23 %y 2 

19 9 


Ft. in. 

10 
12 6 

9 10 

9 10 

12 3J4 

12 3i4 
9 10 
9 10 

11 6 
14 434 

17 3 
14 4H 
17 3 
16 5>A 
19 9 

23 oy 2 

19 9 

16 sy 2 

19 9 

23 m 

19 6 


Inches. 

3by3by-ft 

3by3by -h 

3by3byJ4 

3by3byJi 

3ry3byJ4 • 

3by3byJ4 

3by3by & 

3by3by^ 

3Y 2 by iy 2 by M---- 
3^by3^byM--- 

3Y 2 by zy 2 by H---- 
3J4by3^byA-... 
3J4by3}4byA---- 

4by4by U 

4 by 4byM 

4 by 4by% 

4by4by% 


Inch. 

H 

a 
a 
a 
a 

a 
a 
a 

« 

a 

a 
a 
a 

H 

a 

IS 

a 
a 
a 

a 


13,820 










10,980 






D2 


11,620 
12, 400 






D3 








DX3 


9,760 
8,500 






D4 












DX4 


13, 700 

13, 600 

9,420 






D5 








DX5 








D6 


10,300 






D7 




6,520 








D8 




9,000 




D9 




6,130 




D10 




5,960 




El 




4,530 




E2 










5,000 


E3 






4,280 




E4 




6,580 




E5 




4,980 




E6 










4,270 


E7 






3,930 




E8 

Average. 


12,400 


8,720 


5,060 


4,630 



656 



Technologic Papers of the Bureau of Standards. [Vol. 16 



TABLE 7. — Results of Compression Tests on Angles with Two or More Bolts in 

Each Leg. 



■A-P- 









-1- 

Fig. ii. 
Specimens No. D11-D21. 



*mm$w& 



-L- 

Fig. 






12. 



Specimens No. D22-D37. 



Fig. 13. 
Specimens No. E10-E12 



*H 



'tasters 

-TFT r-f -j , j-i's 4^.a.> 



Fig. 14. 
Specimens No. E14-E20. 




Fig. 15. 
Specimens No. E21-E32. 



Specimen No. 



Length 


Distance 


L. 


M. 


Ft. in. 


Ft. in. 


5 5*3 


4 9*3 


7 11*3 


7 3*3 


5 4*3 


4 8*3 


7 10 


7 2 


7 10 


7 2 


10 1*3 


9 5*3 


9 1 


8 5 


9 1 


8 5 


11 11*3 


11 3*3 


11 11*3 


U 3*3 


11 9*3 


ll 1*3 


3 2 


2 1 


3 1*3 


2 0*3 


3 4 


1 10 


5 7 


4 6 


3 6 


1 7 


6 4 


4 5 


6 4 


4 5 


3 9 


2 3 


6 5 


5 4 


3U*3 


2 0*3 


7 8 


5 4 


7 8 


5 4 


4 2 


1 10 


6 7*3 


5 1*3 


6 7*3 


5 1*3 


4 4 


1 7 


4 4 


1 7 


6 9 


4 10 


6 9 


4 10 


13 7 


13 


13 7 


13 


13 7 


13 


7 2 


6 3 


4 2*3 


2 7*3 


10 5*3 


9 6*3 


7 5 


5 10 


6 2*3 


3 11*3 


15 5*3 


14 6*3 


20 3 


19 4 


4 0*3 


2 9*3 


7 4 


6 1 


4 4*3 


2 5*3 


7 4 


6 1 


4 8 


2 1 


10 8 


9 5 


6 4 


3 9 


10 11 


9 


15 6 


14 3 


6 11*3 


3 0*3 


6 11*3 


3 0*3 


11 2 


8 7 


12 6 


8 7 



Size angle. 



Distance 
N. 



Distance 
K. 



Dll.. 
D12.. 
D13.. 
D14.. 
D15.. 

D16.. 
D17.. 
D18.. 
D19.. 
D20-. 

D21.. 
D22.. 
D23.. 
D24.. 
D25.. 

D26.. 
D28.. 
D28A 
D29.. 
D30.. 

D31.. 
D33.. 
D33A 
D34.. 
D35.. 

D35A 
D36.. 
D36A 
D37.. 
D37A 

E10.. 
Ell.. 
E12.. 
E14.. 
E15.. 

E16.. 

E17.. 
E18.. 
E19.. 
E20.. 

E21.. 
E22.. 
E23.. 
E24.. 
E25.. 

E26.. 
E27.. 
E28.. 
E29.. 
E30.. 

E30A 
E31.. 

E32.. 



Inches. 

3by3byA 

3by3by* 

3by3by*i 

3by3by*£ 

3by3byA 

3by3byJ3 

3*3by3*3byM 

3*3by3*3byA 

3*3by3*3byA 

3*3 by 3*3 by^ 

3*3 by 3*3 by *3 

3by3by-& 

3by3byM 

3by3by-ft 

3by3by*v 

3by3by% 

3by3byJi 

3by3by% 

3*3by3J4byM 

3*3by3*3byM 

3*3by3*3byA 

3*3by3*3byA 

3*3by3*3byA 

3*3by3*3by% 

3*3by3*3by% 

3*3 by 3*3 by % 

3*3 by 3*3 by *3 

3*3 by 3*3 by *3 

3*3 by 3*3 by *3 

3*3 by 3*3 by *3 

4 by 4 by M 

4by4byA 

4 by 4by % 

4 by 4by*£ 

4 by 4 by ^ 

4by4byJi 

4by4by*3 

6 by 6 by Y s 

6by6by% 

6 by 6 by *3 

4 by 4by *£ 

4by4byA 

4 by 4 by % 

4by4by% 

4by 4by *3 

6 by 6by% 

6 by 6by *3 

6 by 6by *3 

6 by 6by *3 

6 by 6 by % 

6by6byM 

6by6byM 

6by6byM 



Inches. 

m 

m, 
m 

m 
m 
m 
m 
m 

m 
1% 

m 

1M 

m 
\% 

1M 

m 

m 

m 

m 

m 

1*3 
1*3 
1*3 
1*3 
•1*3 

1*3 

1*3 
2*3 
2*3 
2*3 

1*3 
1*3 
1*3 
1*3 
1*3 

2*3 
2*3 
2*3 
2*3 
2*3 

2*3 
2*3 
2*3 



Inches. 



m 

2*i 
2*i 






2*i 
2*i 
2M 
2M 
2K 

2H 
2*i 
2*i 



Stang 
Strkkenbergi 



Compression Tests of Structural Angles. 



657 



TABLE 7. — Results of Compression Tests on Angles with Two or More Bolts in 

Each Leg — Continued. 



Specimen No. 


Diam- 
eter of 


Number 

of holes 

in each 

leg. 


Maximum load (lbs. /in.-) for slender- 
ness ratio l/r= 




holes. 


50 


100 


150 


200 


Dll 


Inch, 
ft 

ft 

ft 
S 

ft 

h 
ft 
a 
ft 
ft 

ft 
« 
a 
ft 
ft 

ft 

ft 
ft 
ft 

ft 

H 
ft 

ft 
ft 

ft 
ft 
ft 
ft 
u 


2 
2 
2 
2 
2 

2 
2 
2 
2 
2 

2 
3 
3 
4 
3 

5 
5 
5 
4 
3 

5 
6 
6 

6 
4 

4 
7 
7 
5 
5 

2 
2 
2 
3 

5 

3 
5 
7 
3 
3 

4 
4 
6 
4 
8 

4 
8 
6 
4 
12 

12 
8 

12 




36, 800 






D12 




26,050 




D13 




32, 400 




D14 




29, 900 
29,900 




D15 








D16 






22,700 


D17 






25,000 
25,000 


D18 








D19 






17, 700 
19,900 

15, 800 


D20 








D21 • 








D22 


41,000 
35,500 
36,000 

35,500 






D23 








D24 








Des 


35,300 






D26 






D28 


33, 800 
31,600 






D28A 








D29 


35, 000 






D30 


33,000 






D31 


36,000 








34,000 
35, 700 






D33A 








D34 


38,000 






D3S 


34,900 
34,000 






D35A 








D36 


41,800 
41,200 






D36A 








D37 


34, 100 
33, 900 






D37A 








E10 




ft 
ft 
ft 
ft 
ft 

ft 

n 






14,250 
16, 700 


Ell 








E12 








20, 150 


E14 




33, 500 






E15 


37,000 






E16 




25, 600 




E17 




30,000 




E18 


ft 
ft 
ft 

ft 
ft 

IX 

18 

ft 
ft 

ft 

ft 
ft 
ft 
ft 

ft 
ft 

it 


31, 600 






E19 


* 


22,800 




E20 






20,000 


E21 


37, 500 








E22 


34,480 






E23 


36, 200 






E24 


33,000 






E25 


31,000 






E26 


30, 200 






E27 


28,300 






E28 


27,900 






E29 




27, 750 




E30 


31, 700 
32, 150 






E30A 








E31 


35,000 
28,820 






E32 





















109714°— 22- 



658 Technologic Papers of the Bureau of Standards. 

TABLE 8. — Results of Tests on Coupon Specimens. 



[Vol. 16 



Test numbers. 



Size angle. 



Chemical analysis 
(per cent). 



C. Mn. 



P. 



Yield 
point. 



Tensile 

strength. 



Elon- 
gation 

in 8 
inches. 



Re- 
duc- 
tion of 
area. 



Bl, B2, B3, B4, CI 

B6,B7,C2 

B8, B9, BIO, C3, C4 

Bll, B12, C5, C6 

B13, B14, B15, B16, C7, 
C8, C9, CIO. 

B17, B18, Cll, C12 

B19, B20, B21, C13, C14. 

B22, CIS, C16 

B23, B24, B25, C17, C18. 
B26, B27, B28, C19, C20. 

A1,A2,A3,B29,C21,D1, 
D2, Dll, D12, D22. 

A4, A5, A6, A7, A8, A9, 
A10, B30, B31, B32, 
C22, C23, D3, D4, D13, 
D14, D23. 

C24, C25 D5, D1S, D24, 
D25. 

D16,D26,D28 

B33, B34, C26, C27 

All, A12, A13, B35, B36, 
C28, C29, D6, D7, D8, 
D17, D29, D30. 

C30, D9, D10, D18, D19, 
D31, D33. 

D20.D34.D35 

D21,D36,D37 

El, E2, E3, E9, E10, E14, 

E21. 

E4, Ell, E15, E22 

E5, E6, E7, E12, E16, 

E23, E24. 
E8, E17, E25 

E13, E18, E19, E26 

E20, E27, E28, E29 

E30.E31.E32 

B37, B38, B39, C31 



Inches. 

l}by l}by J. 
1} by 1} by A- 
11 by 11 by}. 
l}byllby&. 
2by2by}.... 



2by2by&-.- 
21 by 21 by}.. 

2iby2JbyA- 
2| by 21 by}.. 
3 by 3 by J.... 



3 by 3 by A... 
3 by 3 by}.... 



3 by 3 by A--- 

3by3by§.... 
31 by 34 by &. 

31 by 31 by }. 



31 by 3} by &. 

3J by 3J by |.. 

31 by 31 by 1.. 

4 by 4 by} 



4 by 4 by &. 
4 by 4 by §.. 

4 by 4 by \.. 

6 by 6 by %.. 
6 by 6 by }. . 
6 by 6 by f. . 
31 by 21 by}. 



Lbs./in." 



Lbs./in. 2 



Per ct. 



Perct. 



0.18 
.20 
.22 
.19 



.17 



0.43 
.49 
.57 
.49 



.48 



.22 
.22 



.18 



.21 
.21 



.21 



.25 

.21 
.24 
.22 
.21 



0.018 
.016 
.015 
.039 



.014 
.016 
.018 



0.036 
.049 
.043 
.045 



.036 
.040 
.034 



38, 160 
38,480 



61,020 
60, 640 



27.5 
28.7 



.40 
.41 

.36 

.34 
.36 



.016 
.024 

.036 

.012 
.025 



.045 
.042 

.044 

.040 
.040 



46,68Q 
37,320 
36,710 

36,080 

36, 840 
38,000 



58,730 
62, 300 
58,020 

58,980 

65, 540 
57,930 



28.2 
30.0 
28.7 

30.0 

27.5 
28.7 



.44 



.011 

.016 
.015 

.020 



.037 



38,020 

37,830 
38,720 

35,850 



60,500 

60,080 
61,980 

58,600 



27.5 

26.2 
27.5 

26.2 



.53 

.43 
.39 
.40 
.35 



.013 

.014 
.013 
.032 
.015 



.040 

.046 
.031 
.040 
.030 



35,780 

36,200 
36, 520 
36, 890 
36,870 



64,750 

57,920 
60,090 
62,950 
60,780 



30.0 

30.0 
28.7 
28.7 
27.5 



58.6 
56.0 



57.4 
54.0 
55.7 

53.2 

49.6 
52.8 



57.2 

55.8 
55.0 

52.2 



50.9 

53.9 
52.9 
52.8 
52.1 



Stang \ 

Strickeriberg J 

TABLE 9.- 



Compression Tests of Structural Angles. 



659 



-Comparison of Lateral Deflection to Strength of Angles with One Bolt 
Connection. 





Slender- 
ness 
ratio. 


Lateral 
deflection 
at 4/9 S. 


Rank. 


Specimen No. 


By 

strength. 


By deflec- 
tion. 


Differ- 
ence in — 


Bl 


1/r 
200 
200 
200 
200 
250 

250 
250 
250 
250 
250 

250 
250 
250 
250 
300 

300 
300 
300 
300 
300 

300 
300 
300 
300 
300 

300 
300 
300 
300 
300 

300 
350 
350 
350 
350 

350 
350 
350 
350 


Inch. 

0.11 
.06 
.17 
.16 
.10 

.20 
.23 
.19 
.19 
.33 

.25 
.31 
.25 
.32 
.13 

.15 
.16 
.15 
.17 
.24 

.54 
.25 
.20 
.73 
.21 

.24 
.32 
.23 
.20 
.40 

.49 
.36 
.27 
.42 
.64 

.15 
.21 
.50 
.20 


3 
1 

4 
2 
1 

8 

3-5 

3-5 

2 

10 

3-5 
7 
6 
9 
2 

3 

5 

1 

8-10 

6-7 

16 

8-10 

4 

17 

12 

13 
11 

6-7 

8-10 

14 

15 
7 
2 
8 
S 

3 
4 
6 

1 


2 
1 
4 
3 
1 

4 

5 

2-3 

2-3 

10 

6-7 
8 

6-7 
9 
1 

2-3 
4 

2-3 

5 

10-11 

16 

12 

6-7 

17 

8 

10-11 

13 

9 

6-7 

14 

15 
5 
4 
6 
8 

1 
3 
7 
2 


1 


B6 





B8 





Bll 


1 


B9 





B13 


4 


B17 





B19 





B23 





B26 





B30 


1 


B38 


1 


BX30 





B37 





B2 


1 


B7 





BIO 


1 


B12 


1 


B14 


3 


B18 


3 


B20 





B22 


2 


B24 


2 


B27 





B29 


4 


B29A ■. 


2 


B31 


2 


BX31 


2 


B33 


1 


B35 





B38 





B21 


2 


B25 


2 


B28 


2 


B32 


3 


BX32 


2 


B34 


1 


B36 


1 


B39 


1 







660 Technologic Papers of the Bureau of Standards. [Vol. 16 

TABLE 10. — Comparison of Lateral Deflection to Strength of Angles with Two Bolt 

Connections in One Leg Only. 



Specimen No. 


Slender- 
ness 
ratio. 


Lateral 
deflection 
at 4/9 S. 


Rank. 


By 

strength. 


By deflec- 
tion. 


Differ- 
ence in — 


C4 


1/r 
150 
150 
150 
150 
150 

150 
150 
150 
150 
150 

200 
200 
200 
200 
200 

200 
200 
200 
200 
200 

200 
200 
200 
200 
200 

200 
250 
250 
250 
250 

250 
250 
250 


Inch. 
0.12 
.10 
.23 

.17 
.32 

.25 
.20 
.23 
.27 
.25 

.19 
.13 
.24 
.20 
.29 

.26 
.24 

.24 
.26 
.24 

.27 
.23 
.25 
.35 
.30 

.19 
.27 


2 
1 
7 
3 
9 

4 
5 
10 
8 
6 

1 
2 
13 
3 
5 

16 
8 
4 

11 
7 

9-10 

6 

12 

15 

14 

9-10 

1 

4-5 

4-5 

7 

6 
3 

2 


2 
1 
5 
3 
9 

6-7 

4 

10 

8 

6-7 

2-3 
1 

6-9 

4 

14 

12 
6-9 
6-9 

11 
6-9 

13 
5 
10 
16 
15 

2-3 

1 
4 
2 
7 

5 
6 
3 





C6 





C7 


2 


Cll 





C13 





C15 


2 


C17.. 


1 


C19.. 





C22 





C22A 





C8 


1 


C12 


1 


C14 


4 


C16 


1 


C18 


9 


C20 


4 


C21 





C21A 


2 


C23 





C23A . 





C24 


3 


C24A . . 


1 


C26 


2 


C28 


1 


C28A 


1 


C31 


6 


C25 





C25A 




C27 


.30 
.64 

.32 
.35 

.31 


2 


C29 





C29A 


1 


C30 


3 


C30A 


1 







TABLE 11. — Comparison of Lateral Deflection to Strength of Angles with Two Bolt 
Connections, One Bolt in Each Leg. 



Specimen No. 


Slender- 
ness 
ratio. 


Lateral 
deflection 
at 4/9 S. 


Rank. 


By 

strength. 


By deflec- 
tion. 


Differ- 
ence in — 


D1...J 


1/r 
200 
200 
200 
200 
200 

200 
250 
250 
250 
250 

250 
250 
250 
300 

300 
300 
300 
300 

300 
350 
350 


Inches. 

0.10 
.24 
.08 
.05 
.09 

.47 
.10 
.18 
.10 
.10 

.10 
.46 
.35 
.27 

.48 

.35 
.81 
.31 

1.05 
.22 
.35 


1 
5 
4 
2 
3 

6 
1 
3 
5 
2 

4 
7 
6 
1 

2 
4 
5 
3 

6 
1 
2 


4 
5 
2 
1 
3 

6 
1-4 

5 
1-4 
1-4 

1-4 
7 
6 
1 

4 
3 

5 
2 

6 
1 
2 


3 


D3 





DX3 


2 


D5... 


1 


DX5 





D6 





D2 





D4 


2 


DX4 


1 


D7. t 





D9 





El 





E5 





D8 





D10 


2 


E2 


1 


E4 





E6 


1 


E8 





E3 





E7 










Stang j 

Slrickevberg J 



Compression Tests of Structural Angles. 



66 1 



TABLE 12. — Comparison of Lateral Deflection to Strength of Angles with Two or 

More Bolts in Each Leg. 





Slender- 
ness 
ratio. 


Lateral 
deflection 
at 4/9 S. 


Rank. 


Specimen No. 


By 

strength. 


By deflec- 
tion. 


Differ- 
ence in — 


Dll 


1/r 
100 
100 
100 
100 
100 

100 
100 
100 
100 
100 

100 

100 
100 
100 
100 

100 

100 
100 
100 
100 

150 
150 
150 
150 
150 

150 
150 
150 
200 
200 

200 
200 
200 
200 
200 


Inch. 

0.03 
.05 
.05 
.09 
.05 

.05 
.05 
.04 
.05 

.05 

.05 
.05 
.05 
.08 
.02 

.08 
.30 


1 

15 

3 

11 

16 

13 
8 
2 
5 
9 

7 

10 
12 
18 

6 

14 
17 
20 
4 
19 

4 
1-2 
1-2 
6-7 
6-7 

5 
8 
3 
1 
4 

3 
6 

7 
5 
2 


2 

5-14 

5-14 

17 

5-14 

5-14 
5-14 
3 
5-14 
5-14 

5-14 

5-14 

5-14 

16 

1 

15 
19 
20 
4 
18 

4-5 
1 
3 

4-5 
2 

6 

7-8 

7-8 

4 

6 

2 
5 
7 
3 
1 





D13 


1 


D25 


2 


D28 


6 


D28A 


2 


D30 





D33 





D33A 


1 


D35 ". 





D35A 





D37 





D37A 





E14 





E17 


2 


E22 


5 


E24 


1 


E26 


2 


E28 




E31 






E32 


.12 

.10 
.05 
.09 
.10 
.06 

.15 
.22 
.22 
.10 
.16 

.05 
.12 
.19 

.07 
.03 


1 


D12 





D14 





D15 


1 


D17 


1 


D18 


4 


E16 


1 


E19 





E29 


4 


D16 - 


3 


D19 


2 


D20 


1 


D21 


1 


E10 





Ell 


2 


E12 


1 







TABLE 13. — End Fixation Factors for Various End Connections of Angles. 



End connection. 


Fixation 
factor. 


End connection. 


Fixation 
factor. 




1.9 
1.5 
1.3 




1.3 




One bolt 


1.1 






1.1 









III. RESULTS AND DISCUSSION OF TESTS. 

(a) General Discussion. — The value of the maximum load 
sustained by each column was measured. These values are given 
in Tables i to 7, inclusive, and have been plotted against the 
values of the slenderness ratio Ijr in Figures 16 and 17. In these 
figures the average value of the maximum loads for each slender- 
ness ratio is shown by a solid circle. Full lines connect these 
average values. It will be noted from Figure 17 that for any 
given slenderness ratio the individual results are quite scattered, 
and when conclusions are drawn from the average values this fact 
must be kept in mind. 



662 



Technologic Papers of the Bureau of Standards. [va. 16 



The manner in which the angles were held in the testing machine 
exerted a great influence on their strength. In other words, the 
strength of a column varies with the "degree of end fixation." 
The amount of this " end fixation " may be expressed by a fixation 
factor / = l/L, where / is the actual length of the member and L the 
length of the round end member which would fail under the same 
load; i.e., the "free length" of the member. Thus, the end fixa- 
tion factor would be 1.0 for a column with round ends and 2.0 for 
a specimen tested with fixed ends. 

The angles with square ends that were placed directly between 
the head and base of the testing machine would thus have an end 







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/SO . 2.00 .2 SO 

s/enaerness ralio 
Fig. 16. — Relation of maximum load to slenderness ratio. 

fixation of approximately the same degree as a column with 
theoretically fixed ends under axial loading, while specimens that 
were held with one bolt in one leg would be expected to approx- 
imate a round-end specimen under eccentric loading. When 
more than one bolt is used, the fixation factor would increase and 
approach 2.0 as the limit for the most rigidly held columns. End 
fixation factors for various end connections are given in Table 13. 
It must be pointed out that in such column tests there is always 
present some eccentricity, due to imperfect centering in the test- 
ing machine and also to the manner in which the load is applied 
to the specimen, as by bolted connections. It is very difficult 
to accurately center even a short compression test specimen. 
The load was eccentric for all the angles bolted to their end con- 



Slang 
Slrickenberg J 



Compression Tests of Structural Angles. 



663 



nections, and this eccentricity of loading always produces a 
diminution of the maximum load. 

The results of the tests were compared with several types of 
column formulas. Formulas of the Rankine-Gordon type repre- 
sent the results fairly well for values of the slenderness ratio up 
to about 150, but the longer column results are evidently best 
represented by the Euler formula: 

P i?E 



where 



and 



P = total load, pounds. 

a = cross-section area, square inches. 
E= modulus of elasticity, pounds per square inch. 

I = length of column, inches. 

r = radius of gyration, inches. 

/ = fixation factor. 





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Fig. 17. — Relation of ■maximum load to slenderness ratio for fixation factor j '=1.5. 

The Kuler formula does not give the strength of short columns, 
however, since for such lengths the elastic limit of the material is 
passed before the column fails. The theory of the deviation of 
short columns from Kuler's law has been worked out by Considere 
(K. Considere, Resistance des Pieces Comprimees, Comptes 
Rendus, Congres International des Precedes de Construction, pp. 
371-397, 1891), Jasinsky (Jasinsky, Zu den Knickfragen, Schweiz. 
Bauzeitung, vol. 25, p. 172, 1895), and Karman (Theo. von Kar- 



664 Technologic Papers of the Bureau of Standards. [Vol. 16 

man, Untersuchung iiber Knickfestigkeit, Forschungsarbeiten 
a. d. Gebiete d. Ingenieurwesens, No. 81, 1910), and later inde- 
pendently by Southwell (R. V. Southwell, The Strength of Struts, 
Engineering, vol. 94, pp. 248-250, 191 2; Aircraft Engineering, 
vol. 1, p. 20 et seq., January, 1920). The theoretical curve given 
by Karman for a steel whose physical properties had been de- 
termined were recalculated for a yield point of 37,000 lbs. /in. 2 and 
a modulus of elasticity of 30,000,000 lbs. /in. 2 They were found 
to agree with the results of these tests when the end fixation 
factor was taken into account and the effect of eccentricity noted. 
This curve, which goes over into the Euler hyperbola for large 
values of the slenderness ratio, has been plotted for comparison 
with the average results of this test. 

In Figures 16 and 17 the dashed curves represent the Euler 
formula for round and for fixed ends, as shown. The dash-and- 
dot curves shown represent the intermediate degree of end fixa- 
tion for the Euler and their dotted continuation for the Karman 
values that seemed to best fit the particular case. 

Karman made a special study of the effect of eccentric loading 
in column testing. It should be noted that the unit stresses he 
found are those from tests on 0.50 per cent carbon steel. The 
important feature is that a small eccentricity has the greatest 
effect in reducing the maximum unit load for values of slender- 
ness ratio from 80 to 85 for round end columns (/ = 1 .0) , and this 
is probably true for the milder steel in these angles. For other 
degrees of end fixation the critical slenderness ratio is obtained 
by multiplying, say, the value 85 by the value of /. It will be 
seen in the detailed discussion that the average value of the max- 
imum unit load falls below the Karman-Euler curves for these 
slenderness ratios, thus denoting the presence of eccentricity. 

Since the lateral deflection at mid height of the columns was 
measured during the tests, it is possible to obtain a rough com- 
parative measure at least of the eccentricity of the test specimens. 
For a column with fixed ends there can be no effective eccentric 
loading. The load, no matter how far its point of application is 
from the centroidal axis of the column, can only produce such 
stresses in a fixed end specimen as would be produced by a load 
concentrically applied. The reason for this is that the definition 
of a "fixed end" column presupposes that the tangent to the 
elastic curve at one end is parallel to and remains parallel to the 
tangent at the other end. In a testing machine, if the columns 
were really to have fixed ends, the bearing plates would remain 



suu*e«berg] Compression Tests of Structural Angles. 665 

parallel to each other throughout the test, and all effects of the 
eccentric loading would be taken up by the supporting screws of 
the testing machine. As a matter of fact, however, it is impos- 
sible to maintain this theoretical condition of fixed ends under an 
eccentric load either in a testing machine or in a built-up structure, 
and the column strength will be reduced if the load is applied 
eccentrically. 

From the elastic theory one may express the relation between 
the lateral deflection at mid height, y ra , and the initial eccentric- 
ity, y a , for round end columns, as follows: 



a l CO! 



y™ = yA ~^J_ i—^ 1 

2r\dE 

where P 1 is the load which produced the deflection y m . Now, 
there is some value of P 1 = kP (P being the value of the maximum 
load from Euler's formula) for which the lateral deflection y m is 
equal to the initial eccentricity y a . Solving for k under this con- 
dition, k = 4/9. That is, in a perfectly elastic round end column 
of any slenderness ratio the deflection at mid height when the 
load is 4/9 of the theoretical maximum is equal to the initial 
eccentricity of load. For other degrees of end fixation this ratio 
would be different, but for the sake of comparison Tables 9 to 1 2 
show the lateral deflection at mid height which occurred at the 
unit loads S 1 = 4/9 S. It is assumed that the value of the theoretical 
unit load 5 is given by the dash-and-dot curves of Figures 16 and 
17. Any other definite ratio might have been chosen for the com- 
parison, provided the ratio were small enough, but the compara- 
tive results would have been practically the same. No claim is 
made that these values represent the actual initial eccentricity. 
It is, however, evident that in practically all cases the specimen 
of given slenderness ratio and degree of end fixation which sus- 
tained the highest unit load also suffered the least lateral deflection 
at the unit load S 1 , while the specimen which suffered the greatest 
lateral deflection sustained the least unit load. Tables 9 to 12 
also give the "rank" of the specimens according to strength and 
to lateral deflection. With very few exceptions the rank of a 
specimen is practically the same by either method of ranking. 

One might conclude, then, from these results that the theoretical 
load-slenderness ratio curve for zero eccentricity should be drawn 
somewhat above the largest load values, and thus obtain a differ- 
ent value of fixation factor from the value obtained by considering 
the mean of the test results. It must, however, be pointed out 



666 Technologic Papers of the Bureau of Standards. ivoi. 16 

that the specimens closely represented the conditions in actual 
construction, and no better centering of a member would be ob- 
tained on the average than was obtained in these tests. The 
mean results are therefore of more importance in design than any- 
such theoretically determined values would be. 

(b) Detailed Discussion of Results. — Figure 16 shows the 
results of tests of angles with square ends. The average result 
line is close to the fixed end curve (dotted) , but agrees still better 
with the dash-and-dot curve plotted for /= 1.9. At ljr = 200 the 
average result is below the curve, and it is in this region that the 
most marked effects of eccentric loading are to be expected. 

When the angles were tested with one bolt connection — in one 
leg only, approximately round end columns, — the results are close 
to the curve of end fixation, for /= 1.1. No appreciable effect of 
eccentricity in loading in reducing the maximum load appears 
here in the average results because the slenderness ratio is so much 
greater than 85. 

The results of tests of angles with folded ends, do not fall so close 
to the curve for /= 1.1 as did those just considered. So few speci- 
mens of this class were tested that it is impossible to draw any 
definite conclusion whether this type of column curve is suitable for 
angles with ends folded. It must also be noted that angles with 
ends folded, as shown in Figures 3, 6, and 8, have a variable radius 
of gyration from section to section. The ordinary column formulas 
are not derived for such conditions. 

Figure 16 shows also the results of the tests of specimens held 
at each end with two bolts, in one leg only. This manner of fas- 
tening is more rigid than when a single bolt is used and the results 
for the columns with slenderness ratio as large as 200 lie close to 
the Euler curve for f=i.7,. For shorter columns the average 
results He below this curve, and this may be due to the eccentric 
loading which would have the greatest effect at l\r= no. 

When two bolts are used, one in each leg, the degree of end 
fixation appears to be the same as for the previously considered 
class, and the results fall very close to the Euler curve for /= 1.3. 
The lengths tested in these two classes overlap for the slenderness 
ratios 200 and 250, and the average results for each of these 
slenderness ratios are nearly equal. The strength of the angles 
held with two bolts, in one leg only, is apparently the same as for 
specimens held with two bolts, one in each leg. 

When two or more bolts were used in each leg for fastening 
the angle to the testing machine, the end fixation factor is still 



st?u%enberg] Compression Tests of Structural Angles. 667 

larger, and the curve for / = 1 .5 of the Karman-Euler type repre- 
sents the average results very well, as shown in Figures 16 and 
17. Here, again, the eccentricity lowers the average result value 
at the critical slenderness ratio value, 85x1.5 = 127.5, and is 
visible at l/r = 150. When angles are held as rigidly as these 
were, it might have been expected that the end fixation factor 
would have been closer to the fixed end condition, / = 2.o. It 
may be that the factor is no higher than 1.5 because of the 
deformation which doubtless occurred in the structural members 
to which the test pieces were bolted. 

IV. CONCLUSIONS. 

1. The values of the maximum unit load in these tests vary 
over a considerable range for any given slenderness ratio and 
manner of fastening the angles in the testing machine. 

2 . In most cases the specimen which sustained the greatest unit 
load for a given slenderness ratio and method of fastening suffered 
the least lateral deflection and the angle which bent most sus- 
tained the lowest unit load at failure, the deflection being meas- 
ured at 4/9 of the theoretical maximum load. 

3. For large slenderness ratios the average values are well 
represented by Euler's formula for long columns, calculated for 
different values of the end fixation factor. 

4. The Karman curves, recalculated for a yield point of 37,000 
lbs. /in. 2 and modulus of elasticity of 30,000,000 lbs. /in. 2 represent 
the average results for small slenderness ratios for several methods 
of end fixation, except in the neighborhood of l/r = 80 to 85 , where 
the effect of eccentricity was greatest. The values of the end 
fixation factor are given in Table 13. 

5. For angles with ends folded the column formulas considered 
do not represent the results found in this series of tests. 

6. It is believed that these values of end fixation factor are of 
importance in the design of structures where the end conditions 
approximate those used in these tests, no matter what formula 
the designer prefers to use. 

7. Eccentricity of loading produces a diminution of column 
strength. In these tests the greatest effect of eccentricity was 
observed in the neighborhood of a "free length" corresponding 
to l/r = 85, which agrees with the results of Karman's investi- 
gations. 

Washington, April 12, 1922. 



